Swing-up control of the cart-pendulum system based on discrete mechanics

In this paper, we develop a new swing-up control strategy for the cart-pendulum system via discrete mechanics. The swing-up control law consists of the swing-up and stabilization stages. In the swing-up stage, we design a controller based on a discrete Lyapunov function. Then, we use a stabilizing controller based on the linearized system and discrete-time optimal regulator theory in the stabilization stage. Moreover, transformation methods from discrete control inputs into continuous zero-order hold inputs are derived. From simulation results, it turns out that the cart-pendulum system is swung up and stabilized by our new method.